Special: The WurmStat

Special: The WurmStat

TL;DR:

Don't count on the damage reduction saving your "tail" very often - but it is a nice bonus that adds to the already solid survivability of the Trichinosis Team.

A Mistake and A Warning

Oops, wrong button.

In our last article, we mentioned that there might be some times when it's beneficial to put Substance Siphon on Fecula, even if it didn't increase the number of dice that she's rolling on defense.  We arrived at that conclusion by doing a few specific calculations on attacks and defenses and factoring in the damage reduction ability of the Wurmstat.  In these specific cases, there were very slight improvements to the average damage Fecula would take against those attacks.  Upon realizing this, we got very excited to see how much benefit Fecula (and the other Barfbois) would gain from switching to dodges against all attacks.  So we did a prodigious amount of math.

As it turns out, switching from blocks to dodges is a bad idea if you don't also gain dice, even for the Wurmspat.  Unless your opponent's army makes exclusively 2hammer/2damage attacks, you're going to take more damage from swapping blocks for dodges in equal number, despite getting to activate your damage reduction ability significantly more of the time. Bummer. (Note - you are still better off swapping blocks for dodges if you grab an extra die in the process, so Fecula can benefit from Substance Siphon in the 2nd and 3rd rounds, while the Leprosy Lads should wait until round 3.)

However, we did do a bunch of math, and it seems wasteful not to use it for something, so we decided to create a mega-post all about the Wurmspat's damage reduction.  We'd like to go forward with a warning though - there's a lot of math here.  If you're not into that, and you come here for the Letterkenny references and clever wordplay, you might want to skip most of the rest of this article. 

How Often...

The first step in figuring out just how useful the Wurmspat defensive ability is was to see how often it activated against the various attacks in the game.  Unfortunately, this wasn't simply a matter of determining if an attack hit or missed, but rather how it hit or missed.  The faces of the individual dice suddenly mattered, instead of just the totals.  To that end, we fired up anydice, entered a few custom algorithms, and rolled a theoretical butt-ton of dice.

Each separate die attribute on attacks would come up with a different rate for activating the Wurmspat ability, so we had to calculate for each type of attack against each of the Wurmspat defenses.  Some of these calculations were pretty easy, like the one for 1-Sword vs. 1-Block:

1S v 1B		1C	1S	N
		0.1667	0.1667	0.6667
1C	0.1667	2.78%	2.78%	11.11%
1B	0.3333	5.56%	5.56%	22.22%
1D	0.1667	2.78%	2.78%	11.11%
N	0.3333	5.56%	5.56%	22.22%

Just like in the last article, we color-coded the results for ease of interpretation.  On green results, your defender takes no damage; on yellow results they reduce the damage by 1; and on red results they take full damage.  Easy, right?

Sure, until you get to things like 4S vs. 2B defenses, which look more like this (with blue results showing 2 points of damage reduction).

4S v 1B		4C	3C+1	3C	2C+2	2C+1	2C	1C+3	1C+2	1C+1	1C	4S	3S	2S	1S	N
		0.0008	0.00308	0.01232	0.004628	0.037024	0.074048	0.0030864	0.0370368	0.1481472	0.1975296	0.0008	0.01232	0.074048	0.1975296	0.1976024
2C	0.0278	0.00%	0.01%	0.03%	0.01%	0.10%	0.21%	0.01%	0.10%	0.41%	0.55%	0.00%	0.03%	0.21%	0.55%	0.55%
1C+1B	0.11112	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.20%	0.01%	0.14%	0.82%	2.20%	2.20%
1C+1D	0.05556	0.00%	0.02%	0.07%	0.03%	0.21%	0.41%	0.02%	0.21%	0.82%	1.10%	0.00%	0.07%	0.41%	1.10%	1.10%
1C	0.1111	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.19%	0.01%	0.14%	0.82%	2.19%	2.20%
2B	0.1111	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.19%	0.01%	0.14%	0.82%	2.19%	2.20%
2D	0.0278	0.00%	0.01%	0.03%	0.01%	0.10%	0.21%	0.01%	0.10%	0.41%	0.55%	0.00%	0.03%	0.21%	0.55%	0.55%
1B+1D	0.1111	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.19%	0.01%	0.14%	0.82%	2.19%	2.20%
1B	0.2222	0.02%	0.07%	0.27%	0.10%	0.82%	1.65%	0.07%	0.82%	3.29%	4.39%	0.02%	0.27%	1.65%	4.39%	4.39%
1D	0.1111	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.19%	0.01%	0.14%	0.82%	2.19%	2.20%
N	0.1111	0.01%	0.03%	0.14%	0.05%	0.41%	0.82%	0.03%	0.41%	1.65%	2.19%	0.01%	0.14%	0.82%	2.19%	2.20%

Even so, once we calculated all of these possible dice permutations, we got a pretty good handle on how often the Wurmspat damage reduction (WDR from here on) would trigger...

On a Related Subject...

There's just one problem (Spoiler Alert: There is more than just one problem): the tables above only tell us how often the WDR will trigger against a specific kind of attack.  To figure out how useful the WDR really is, we have to figure out how often it triggers against an average attack.  Just like in the last article, we'll use a random-average attack method to determine this; and just like in the last article, we're going to trust that GW is still doing a relatively good job of distributing attack stats in a way that makes sense (we've confirmed this in the past, and are going to keep banking on it until evidence to the contrary comes up).  

For this step, we took the frequency of various attacks and multiplied them into the results we got in the above step. Which looks something like this:

1S vs 1B	Rate	Damage
Block	77.78%	0
-1	5.56%	0.064821295
Full	16.67%	0.2778333333
Total	100.01%	0.3426546283

Viola!  Now we now how often the WDR triggers in an average game...

Only, that depends on...

Except that the stupid WDR won't lower the damage done by an attack below 1.  That, of course, greatly complicates the math behind it's effectiveness.  In order to figure this out, you've got to see not only what dice are rolled for every attack in the game, but how much damage those attacks do.  Then you need to factor the frequency of both the dice and the damage into the rates we got above.  It's kind of a hassle.

To do this, we went through every base attack in the game on all 24 currently available warbands and broke them down by dice characteristic and damage. 

		% of range	% of whole
1S-1D	3	50.00%	1.04%
1S-2D	2	33.33%	0.69%
1S-3D	1	16.67%	0.35%
1S-4D	0	0.00%	0.00%
	6		2.08%

Since we did all that work, we might as well share a few factoids about that breakdown while we're here. (Note that we bulked 2-swirl magic attacks in with 2-hammer attacks, since the un-supported odds are the same).  Of the 289 currently available base attacks:

• 2-hammer attacks are the most common die type (n106)
• 2-hammer/2-damage attacks are the most common attacks (n54), followed closely by 2-sword/1damage attacks (n50)
• There is only one 1-sword/3-damage attack (Snirk), only one 2-lightning/1-damage attack (inspired Fecula), and only one 4-sword/2-damage attack (inspired Maiden)
• All of the 4-damage attacks are 2-hammers
• It's a good thing we weren't terribly busy this week

This final piece of data should allow us to actually calculate how useful the WDR is...

Which brings us to...

Just how often does the WDR trigger in a useful way then? 

The following list summarizes our findings:

• With 1 Block Die: 8.58% chance of reducing damage by 1
• With 1 Dodge Die: 14.11% chance of reducing damage by 1
• With 2 Block Dice: 10.89% chance of reducing damage by 1; 0.59% by 2
• With 2 Dodge Dice: 13.33% chance of reducing damage by 1; 1.31% by 2

Do remember, that even though you're more likely to trigger WDR with dodge dice than you are with an equal number of block dice, you're still taking more damage on average.

Summary:

Full Disclosure: The article originally attached to the above image was TL, so we DR.

And so, what have we learned?  Well, the WDR triggers fairly rarely - at a rather disappointing rate, really.  However, it's important to keep in mind that this ability is a bonus, in addition to your normal chance to defend.  And since the Colostomy Crew has pretty good defenses already, this bonus ability does make them just that much harder to kill.